This has caused a lot of confusion... in the book, the sword Narsil (I think it means 'the red and white flame') was reforged befoe Aragorn left Rivendell. He took it with the intent of returning it to Gondor and claiming the kingship. According to sources, Jackson has relocated the reforging of Anduril into The Two Towers. In the movie, Aragorn sets out from Rivendell to protect Frodo, not to reclaim the throne of Gondor as he does in the book - only at the end of the film does he decide to play his part in reuniting the kingdoms of Man. The Sword Anduril will re-appear in the Two Towers.